In this section, we provide a variational interpretation of the estimation of the mutual information using the alpha-parameterized value function introduced in (REF ). Inspired by the \(f\) -divergence variational estimation method proposed in [1]}, we exploit the Fenchel conjugate method to alternatively derive (REF ).
In particular, we show that (REF ) constitutes a lower bound on the mutual information. Its maximization over positive discriminators \(D\)  (as proposed in Lemma 3) leads to the mutual information \(I(X;Y)\) .
